Question: Which of the following numbers is a multiple of 9? ${60,63,71,74,100}$
Explanation: The multiples of $9$ are $9$ $18$ $27$ $36$ ..... In general, any number that leaves no remainder when divided by $9$ is considered a multiple of $9$ We can start by dividing each of our answer choices by $9$ $60 \div 9 = 6\text{ R }6$ $63 \div 9 = 7$ $71 \div 9 = 7\text{ R }8$ $74 \div 9 = 8\text{ R }2$ $100 \div 9 = 11\text{ R }1$ The only answer choice that leaves no remainder after the division is $63$ $ 7$ $9$ $63$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $63$ $63 = 3\times3\times7 9 = 3\times3$ Therefore the only multiple of $9$ out of our choices is $63$. We can say that $63$ is divisible by $9$.